数列的单调性是数列的一类常见问题,数列可以看作是一类特殊的函数,其定义域是正整数集或其子集,而数列的通项公式就是其相应的函数解析式,例如等差数列{an},an=a1+(n-1)d=dn+(a1-d),当d≠0时,可以把an看作是n的一次函数;等比数列{bn},bn=b1·qn-1=a1/qqn,当q>0且q≠1时,可以把bn看作是n的指数函数。因此遇到单纯用数列的方法难以解决的问题时,不妨从数列的函数本质出发,探寻解题切入点,往往可以收到事半功倍的效果。 The monotonicity of a series is a common problem in a series. A series can be considered as a special kind of function whose domain is a set of positive integers or a subset of it. The general formula of a series is its corresponding functional analytic formula, for example The difference sequence {an}, an = a1 + (n-1) d = dn + (a1-d) can be regarded as a linear function of n when d ≠ 0; the geometric sequence {bn}, bn = b1 · Qn-1 = a1 / qqn, when q> 0 and q ≠ 1, we can regard bn as an exponential function of n. Therefore, when encountering problems that are difficult to be solved by simply using series methods, we may proceed from the nature of the functions of the series and explore the entry points for problem solving, which often can achieve the result of multiplier.